{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Learn to Throw\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/docs/Learn_to_Throw_Tutorial.ipynb)\n",
    "\n",
    "In this notebook, we will train a fully-connected neural network to solve an inverse ballistics problem.\n",
    "We will compare supervised training to differentiable physics training, both numerically and visually.\n",
    "\n",
    "[**Φ-Flow**](https://github.com/tum-pbs/PhiFlow)\n",
    "&nbsp;&nbsp;&nbsp; [**Documentation**](https://tum-pbs.github.io/PhiFlow/)\n",
    "&nbsp;&nbsp;&nbsp; [**API**](https://tum-pbs.github.io/PhiFlow/phi)\n",
    "&nbsp;&nbsp;&nbsp; [**Demos**](https://github.com/tum-pbs/PhiFlow/tree/master/demos)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# !pip install phiflow"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "# from phi.tf.flow import *\n",
    "from phi.torch.flow import *\n",
    "# from phi.jax.stax.flow import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "To define the physics problem, we write a function to simulate the forward physics. This function takes the initial position, height, speed and angle of a thrown object and computes where the object will land, assuming the object follows a parabolic trajectory. Neglecting friction, can compute this by solving a quadratic equation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "\u001B[94m11.414213\u001B[0m"
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def simulate_hit(pos, height, vel, angle, gravity=1.):\n",
    "    vel_x, vel_y = math.cos(angle) * vel, math.sin(angle) * vel\n",
    "    height = math.maximum(height, .5)\n",
    "    hit_time = (vel_y + math.sqrt(vel_y**2 + 2 * gravity * height)) / gravity\n",
    "    return pos + vel_x * hit_time, hit_time, height, vel_x, vel_y\n",
    "\n",
    "simulate_hit(10, 1, 1, 0)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Let's plot the trajectory! We define *y(x)* and sample it on a grid. We have to drop invalid values, such as negative flight times and below-ground points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 1 Axes>"
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sample_trajectory(pos, height, vel, angle, gravity=1.):\n",
    "    hit, hit_time, height, vel_x, vel_y = simulate_hit(pos, height, vel, angle, gravity)\n",
    "    t = math.linspace(0, hit_time, spatial(t=100))\n",
    "    return vec(x=pos + vel_x * t, y=height + vel_y * t - gravity / 2 * t ** 2)\n",
    "\n",
    "vis.plot(sample_trajectory(tensor(10), 1, 1, math.linspace(-PI/4, 1.5, channel(angle=7))), title=\"Varying Angle\")"
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "Before we train neural networks on this problem, let's perform a classical optimization using gradient descent in the initial velocity `vel`. We need to define a loss function to optimize. Here we desire the object to hit at `x=0`."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "outputs": [
    {
     "data": {
      "text/plain": "\u001B[94m50.0\u001B[0m"
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vel = tensor(1)\n",
    "\n",
    "def loss_function(vel):\n",
    "  return math.l2_loss(simulate_hit(10, 1, vel, 0)[0] - 0)\n",
    "\n",
    "loss_function(0)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Φ<sub>Flow</sub> uses the selected library (PyTorch/TensorFlow/Jax) to derive analytic derivatives.\n",
    "By default, the gradient function also returns the function value."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "outputs": [
    {
     "data": {
      "text/plain": "(\u001B[94m65.14213\u001B[0m, [\u001B[94m16.142136\u001B[0m])"
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gradient = math.functional_gradient(loss_function, get_output=True)\n",
    "gradient(vel)"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "vel=\u001B[94m-2.2284272\u001B[0m - loss=\u001B[94m65.14213\u001B[0m\n",
      "vel=\u001B[94m-4.1654835\u001B[0m - loss=\u001B[94m23.451168\u001B[0m\n",
      "vel=\u001B[94m-5.3277173\u001B[0m - loss=\u001B[94m8.442421\u001B[0m\n",
      "vel=\u001B[94m-6.0250573\u001B[0m - loss=\u001B[94m3.0392709\u001B[0m\n",
      "vel=\u001B[94m-6.4434614\u001B[0m - loss=\u001B[94m1.0941381\u001B[0m\n",
      "vel=\u001B[94m-6.694504\u001B[0m - loss=\u001B[94m0.39388976\u001B[0m\n",
      "vel=\u001B[94m-6.8451295\u001B[0m - loss=\u001B[94m0.14180061\u001B[0m\n",
      "vel=\u001B[94m-6.935505\u001B[0m - loss=\u001B[94m0.051048037\u001B[0m\n",
      "vel=\u001B[94m-6.9897304\u001B[0m - loss=\u001B[94m0.018377367\u001B[0m\n",
      "vel=\u001B[94m-7.0222654\u001B[0m - loss=\u001B[94m0.0066157645\u001B[0m\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 1 Axes>"
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 864x360 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "trj = [vel]\n",
    "for i in range(10):\n",
    "  loss, (grad,) = gradient(vel)\n",
    "  vel = vel - .2 * grad\n",
    "  trj.append(vel)\n",
    "  print(f\"vel={vel} - loss={loss}\")\n",
    "trj = math.stack(trj, channel('opt'))\n",
    "vis.plot(sample_trajectory(tensor(10), 1, trj, 0))"
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%%\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we can just subtract the gradient times a learning rate $\\eta = 0.2$ until we converge."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Next, we generate a training set and test by sampling random values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def generate_data(shape):\n",
    "  pos = math.random_normal(shape)\n",
    "  height = math.random_uniform(shape) + .5\n",
    "  vel = math.random_uniform(shape)\n",
    "  angle = math.random_uniform(shape) * PI/2\n",
    "  return math.stack(dict(pos=pos, height=height, vel=vel, angle=angle), channel('vector'))\n",
    "\n",
    "x_train = generate_data(batch(examples=1000))\n",
    "x_test = generate_data(batch(examples=1000))\n",
    "y_train = simulate_hit(*x_train.vector)[0]\n",
    "y_test = simulate_hit(*x_test.vector)[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now, let's create a fully-connected neural network with three hidden layers. We can reset the `seed` to make the weight initialization predictable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "DenseNet(\n  (linear0): Linear(in_features=1, out_features=32, bias=True)\n  (linear1): Linear(in_features=32, out_features=64, bias=True)\n  (linear2): Linear(in_features=64, out_features=32, bias=True)\n  (linear_out): Linear(in_features=32, out_features=4, bias=True)\n)"
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.seed(0)\n",
    "net_sup = dense_net(1, 4, [32, 64, 32])\n",
    "net_sup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([-0.0075,  0.5364, -0.8230, -0.7359, -0.3852,  0.2682, -0.0198,  0.7929,\n        -0.0887,  0.2646, -0.3022, -0.1966, -0.9553, -0.6623, -0.4122,  0.0370,\n         0.3953,  0.6000, -0.6779, -0.4355,  0.3632,  0.8304, -0.2058,  0.7483,\n        -0.1612,  0.1058,  0.9055, -0.9277, -0.6295, -0.2532, -0.3898,  0.8640],\n       device='cuda:0')"
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# net_sup.trainable_weights[0]  # TensorFlow\n",
    "net_sup.state_dict()['linear0.weight'].flatten()  # PyTorch\n",
    "# net_sup.parameters[0][0]  # Stax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "For the differentiable physics network we do the same thing again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": "tensor([-0.0075,  0.5364, -0.8230, -0.7359, -0.3852,  0.2682, -0.0198,  0.7929,\n        -0.0887,  0.2646, -0.3022, -0.1966, -0.9553, -0.6623, -0.4122,  0.0370,\n         0.3953,  0.6000, -0.6779, -0.4355,  0.3632,  0.8304, -0.2058,  0.7483,\n        -0.1612,  0.1058,  0.9055, -0.9277, -0.6295, -0.2532, -0.3898,  0.8640],\n       device='cuda:0')"
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "math.seed(0)\n",
    "net_dp = dense_net(1, 4, [32, 64, 32])\n",
    "# net_dp.trainable_weights[0]  # TensorFlow\n",
    "net_dp.state_dict()['linear0.weight'].flatten()  # PyTorch\n",
    "# net_dp.parameters[0][0]  # Stax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Indeed, the We see that the networks were initialized identically! Alternatively, we could have saved and loaded the state."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Supervised Training\n",
    "Now we can train the network. We feed the desired hit position into the network and predict a possible initial state.\n",
    "For supervised training, we compare the network prediction to the ground truth from our training set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised loss (training set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[94m1.563 ± 0.816\u001B[0m \u001B[37m(2e-01...6e+00)\u001B[0m\n",
      "Supervised loss (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[94m1.620 ± 0.860\u001B[0m \u001B[37m(3e-01...7e+00)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "opt_sup = adam(net_sup)\n",
    "\n",
    "def supervised_loss(x, y, net=net_sup):\n",
    "  prediction = math.native_call(net, y)\n",
    "  return math.l2_loss(prediction - x)\n",
    "\n",
    "print(f\"Supervised loss (training set): {supervised_loss(x_train, y_train)}\")\n",
    "print(f\"Supervised loss (test set): {supervised_loss(x_test, y_test)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised loss (training set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[94m0.323 ± 0.229\u001B[0m \u001B[37m(6e-03...2e+00)\u001B[0m\n",
      "Supervised loss (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[94m0.340 ± 0.236\u001B[0m \u001B[37m(2e-03...2e+00)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "for i in range(100):\n",
    "  update_weights(net_sup, opt_sup, supervised_loss, x_train, y_train)\n",
    "\n",
    "print(f\"Supervised loss (training set): {supervised_loss(x_train, y_train)}\")\n",
    "print(f\"Supervised loss (test set): {supervised_loss(x_test, y_test)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "What? That's almost no progress! Feel free to run more iterations but there is a deeper problem at work here. Before we get into that, let's train a the network again but with a differentiable physics loss function."
   ]
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Training with Differentiable Physics\n",
    "For the differentiable physics loss, we simulate the trajectory given the initial conditions predicted by the network. Then we can measure how close to the desired location the network got."
   ],
   "metadata": {
    "collapsed": false,
    "pycharm": {
     "name": "#%% md\n"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised loss (training set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[94m1.275 ± 0.694\u001B[0m \u001B[37m(1e-01...5e+00)\u001B[0m\n",
      "Supervised loss (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[94m1.316 ± 0.729\u001B[0m \u001B[37m(1e-01...5e+00)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "def physics_loss(y, net=net_dp):\n",
    "  prediction = math.native_call(net, y)\n",
    "  y_sim = simulate_hit(*prediction.vector)[0]\n",
    "  return math.l2_loss(y_sim - y)\n",
    "\n",
    "opt_dp = adam(net_dp)\n",
    "\n",
    "for i in range(100):\n",
    "  update_weights(net_dp, opt_dp, physics_loss, y_train)\n",
    "\n",
    "print(f\"Supervised loss (training set): {supervised_loss(x_train, y_train, net=net_dp)}\")\n",
    "print(f\"Supervised loss (test set): {supervised_loss(x_test, y_test, net=net_dp)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "This looks even worse! The differentiable physics network seems to stray even further from the ground truth.\n",
    "Well, we're not trying to match the ground truth, though. Let's instead measure how close to the desired location the network threw the object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "scrolled": true,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Supervised network (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[94m0.004 ± 0.007\u001B[0m \u001B[37m(7e-11...9e-02)\u001B[0m\n",
      "Diff.Phys. network (test set): \u001B[92m(examplesᵇ=1000)\u001B[0m \u001B[94m2.51e-04 ± 4.8e-04\u001B[0m \u001B[37m(6e-11...1e-02)\u001B[0m\n"
     ]
    }
   ],
   "source": [
    "print(f\"Supervised network (test set): {physics_loss(y_test, net=net_sup)}\")\n",
    "print(f\"Diff.Phys. network (test set): {physics_loss(y_test, net=net_dp)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "Now this is much more promissing. The diff.phys. network seems to hit the desired location very accurately considering it was only trained for 100 iterations. With more training steps, this loss will go down even further, unlike the supervised network.\n",
    "\n",
    "So what is going on here? Why does the supervised network perform so poorly?\n",
    "The answer lies in the problem itself. The task is multi-modal, i.e. there are many initial states that will hit the same target.\n",
    "The network only gets the target position and must decide on a single initial state. With supervised training, there is no way to know which ground truth solution occurs in the test set. The best the network can do is average nearby solutions from the training set. But since the problem is non-linear, this will give only a rough guess.\n",
    "\n",
    "The diff.phys. network completely ignores the ground truth solutions which are not even passed to the `physics_loss` function. Instead, it learns to hit the desired spot, which is exactly what we want.\n",
    "\n",
    "We can visualize the difference by looking at a couple of trajectories."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "scrolled": false,
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\PhD\\phiflow2\\phi\\math\\_shape.py:1753: RuntimeWarning: Stacking shapes with incompatible item names will result in item names being lost. Got ('pos', 'height', 'vel', 'angle') and None\n",
      "  warnings.warn(f\"Stacking shapes with incompatible item names will result in item names being lost. Got {item_names[index]} and {items}\", RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 1152x288 with 4 Axes>"
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": "<Figure size 1152x288 with 4 Axes>",
      "image/png": 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\n"
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "predictions = math.stack({\n",
    "    \"Ground Truth\": x_test.examples[:4],\n",
    "    \"Supervised\": math.native_call(net_sup, y_test.examples[:4]),\n",
    "    \"Diff.Phys\": math.native_call(net_dp, y_test.examples[:4]),\n",
    "}, channel('curves'))\n",
    "vis.plot(sample_trajectory(*predictions.vector), size=(16, 4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We can see that the differentiable physics network matches the hit point much more precisely than the supervised network, as expected from the loss values."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}